15 19 25 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 19   c = 25

Area: T = 142.1666056075
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 36.76992608408° = 36°46'9″ = 0.64217446652 rad
Angle ∠ B = β = 49.30774364255° = 49°18'27″ = 0.86105771113 rad
Angle ∠ C = γ = 93.92333027337° = 93°55'24″ = 1.63992708771 rad

Height: ha = 18.95554741434
Height: hb = 14.96548480079
Height: hc = 11.3733284486

Median: ma = 20.8998564544
Median: mb = 18.29661744635
Median: mc = 11.69440155635

Inradius: r = 4.81991883415
Circumradius: R = 12.52993621359

Vertex coordinates: A[25; 0] B[0; 0] C[9.78; 11.3733284486]
Centroid: CG[11.59333333333; 3.79110948287]
Coordinates of the circumscribed circle: U[12.5; -0.85772721461]
Coordinates of the inscribed circle: I[10.5; 4.81991883415]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.2310739159° = 143°13'51″ = 0.64217446652 rad
∠ B' = β' = 130.6932563575° = 130°41'33″ = 0.86105771113 rad
∠ C' = γ' = 86.07766972663° = 86°4'36″ = 1.63992708771 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 15 ; ; b = 19 ; ; c = 25 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 15+19+25 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-15)(29.5-19)(29.5-25) } ; ; T = sqrt{ 20211.19 } = 142.17 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 142.17 }{ 15 } = 18.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 142.17 }{ 19 } = 14.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 142.17 }{ 25 } = 11.37 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 15**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 36° 46'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-15**2-25**2 }{ 2 * 15 * 25 } ) = 49° 18'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-15**2-19**2 }{ 2 * 19 * 15 } ) = 93° 55'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 142.17 }{ 29.5 } = 4.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 36° 46'9" } = 12.53 ; ;




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